List questions from commutative-algebra

Published on 29 Apr 2026 - 12:52

343

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Localization of a non-zero module is non-zero?

Published on 29 Apr 2026 - 12:25

101

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Tensoring by free modules

Published on 14 Apr 2026 - 21:50

617

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Primary ideals in an Artinial local ring

Published on 20 Apr 2026 - 14:11

59

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Primary decomposition in a finite algebra

Published on 27 Apr 2026 - 2:43

200

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A variation of the argument to prove that $\{m/n:n \text{ is odd },n,m \in \mathbb{Z}\}$ is a PID

Published on 05 May 2026 - 18:01

197

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Does every noetherian ring inject into the product of its localizations at primes?

Published on 11 Apr 2026 - 4:13

84

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Extension and restriction of involutions

Published on 29 Apr 2026 - 12:44

408

Views

Every locally closed irreducible subset $Z$ of $X:=\text{Spec}A$ contains a unique generic point.

Published on 05 May 2026 - 0:05

413

Views

Profinite completions and inverse limits

Published on 29 Apr 2026 - 12:49

173

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A relation between prime ideals and ring of fraction.

Published on 29 Apr 2026 - 12:24

244

Views

Exercise on conditions for a ring to be normal

Published on 02 May 2026 - 23:46

59

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Derivations of $K[X]/I$ for $I$ an ideal

Published on 05 May 2026 - 0:05

127

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Let $\varphi : R \rightarrow S$ be a ring homomorphism and $T \subseteq R$. Prove that $\varphi(r)$ is integral over $\varphi(T)$.

Published on 14 Apr 2026 - 0:46

273

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A question concerning the post "Closed points of $\operatorname{Spec}(A)$ are dense"

Published on 11 Apr 2026 - 4:20

List Question

$M$ finitely generated over $(R,\mathfrak{m})\Rightarrow M/\mathfrak{m}M$ artinian

Localization of a non-zero module is non-zero?

Tensoring by free modules

Primary ideals in an Artinial local ring

Primary decomposition in a finite algebra

A variation of the argument to prove that $\{m/n:n \text{ is odd },n,m \in \mathbb{Z}\}$ is a PID

Does every noetherian ring inject into the product of its localizations at primes?

Extension and restriction of involutions

Every locally closed irreducible subset $Z$ of $X:=\text{Spec}A$ contains a unique generic point.

Profinite completions and inverse limits

A relation between prime ideals and ring of fraction.

Exercise on conditions for a ring to be normal

Derivations of $K[X]/I$ for $I$ an ideal

Let $\varphi : R \rightarrow S$ be a ring homomorphism and $T \subseteq R$. Prove that $\varphi(r)$ is integral over $\varphi(T)$.

A question concerning the post "Closed points of $\operatorname{Spec}(A)$ are dense"

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